Everton play Croatian side Hajduk Split in the Europa League playoff round, while AC Milan have been drawn against Macedonian side Shkendija.
Everton, who have invested heavily in players including Wayne Rooney, Sandro Ramirez and Michael Keane this summer, edged past Ruzomberok in the third qualifying round and will now look to secure their place in the group stage.
"Hajduk Split will be a real challenge, with their strong support and a stadium that is good to play football in," coach Ronald Koeman told Everton's website. "But of course we want to reach the group stages of the Europa League, so we will have analysed their strengths and weaknesses between now and the tie and we will be prepared."
In European competition for the first time in three years, Everton were not at their best in either leg against Ruzomberok.
Leighton Baines' deflected shot gave them a 1-0 win at Goodison Park before Dominic Calvert-Lewin's goal on Thursday night provided the same score line in the away leg.
Shkendija vs. AC Milan
Vardar vs. Fenerbahce
Ajax vs. Rosenborg
Osijek vs. Austria Vienna
Crvena Zvezda vs. Krasnodar
Altach vs. Maccabi Tel-Aviv
BATE Borisov vs. Olexandriya
Club Brugge vs. AEK Athens
Maritimo vs. Dynamo Kiev
Dinamo Zagreb vs. Skenderbeu
Ludogorets vs. Suduva
Panathinaikos vs. Athletic Bilbao
Apollon Limassol vs. Midtjylland
Domzale vs. Marseille
Partizan Belgrade vs. Videoton
FH Hafnarfjordur vs. Braga
Everton vs. Hajduk Split
Utrecht vs. Zenit St Petersburg
Legia Warsaw vs. Sheriff Tiraspol
Viitorul vs. Salzburg
Viktoria Plzen vs. AEK Larnaca
PAOK Salonika vs. Ostersund
Hajduk Split have beaten Levski Sofia and Brondby to get to this stage and have lost in the final playoff round in each of the past three seasons.
The last Premier League club to play them were Stoke in 2011 and Tony Pulis' team won each leg to advance 2-0 on aggregate.
Milan, meanwhile, are back in European competition for the first time since 2014 and take on Shkendija, who finished second in the Macedonian league last season.
Ajax, who finished runners-up to Manchester United in last season's Europa League, play Norwegian club Rosenborg after the Dutch giants lost their Champions League third-round qualifier to French club Nice.
Elsewhere, Athletic Bilbao, who reached the final in 2012 but lost out to Atletico Madrid, take on Greek side Panathinaikos.
Marseille will come up against Slovenian side NK Domzale, while Zenit St Petersburg play Eredivisie outfit Utrecht.
All ties will take place on Aug. 17 and 24.